Isothermal* and Adiabatics. be actually measured (see Fig. 325); but as these curves have definite formulae, it is easier to use algebraic methods. Then, y Area of curve having formula PV = C is PV x loge , vi and as PV = cr. and = the ratio of expansion r. v, Area = cr loge r. (Seep. 1131.) (Use hyperbolic logarithms, and see Fig. 612) Area of curve having formula PVW = C is ------?? 71 I Isothermals and Adiabatics.If a gas expand, and advance a piston against a resistance, it does work requiring expenditure of heat. Such heat being abstracted from the gas, the temperature of the latter falls; but if heat be supplied just as fast as it is abstracted, viz. equal to the work done, the tem- perature will remain constant, the expansion be according to Boyle (PV =» C), and the curve be called an isothermal. If no heat be supplied, the pressure-volume curve will fall below the hyperbola, as in Fig. 613, according to the formula PV" = C, and be then termed an adiatiatic. Similarly, in com- pressing, the adiabatic will rise above the isothermal, because the gas becomes t heated by work done upon it (Fig. 614). (See Appendix IL,p. 879.) Adiabatic Exponent.The value of n will now be found for the adiabatic. Area of curve n _ ('I-' External work, Total work = Internal work + External work - <- - '-> -->_+,K-K') - h - o (SSf * Notice change of sign in two places in order to balance.